Probabilistic Analysis of Geometric Uncertainty Effects on Blade-Alone Forced Response

Abstract

This paper investigates the effect of manufacturing variations on the blade-alone forced response of a transonic low aspect ratio fan. A simulated set of coordinate measurement machine measurements from a single rotor, representative of actual manufacturing variations, are used to investigate geometric effects. A reduced order model is developed to rapidly solve for the forced response and is based on eigensensitivity analysis and dynamic response mode superposition. An approximation error analysis is conducted to quantify accuracy of the new tool and errors between approximate and full finite element analysis solutions are shown to be small for low order modes with some high order modes having moderate error. A study of the simulated measured blade results show a significant amount of forced response variation along the leading edge of the airfoil. Statistics from this simulated measured rotor are used with Monte Carlo sampling to generate random blades realizations that are solved with the reduced order model. This procedure allows the prediction of the variation across an entire fleet of blades from a small sample of blades. The large variations predicted, up to 40%, could have a significant impact of the blade design process including the procedures to account for foreign object damage damage tolerance, how non-intrusive stress measurement systems are used, and how mistuning prediction algorithms are validated.